Express cos`320^(@)` as a function of an angle between `0^(@) and 90^(@)`
I. `cos40^(@)`
II. `sin50^(@)`
III. `cos50^(@)`

Options

A. I only
B. II only
C. III only
D. I and II

Explanation

To express \( \cos 320^\circ \) as a function of an angle between \( 0^\circ \) and \( 90^\circ \), we can follow these steps:

### Step 1: Rewrite \( 320^\circ \)
First, we can express \( 320^\circ \) in a more manageable form:
\[ 320^\circ = 360^\circ - 40^\circ \]

### Step 2: Use the Cosine Identity
Using the cosine identity for angles, we know that:
\[ \cos(360^\circ - \theta) = \cos(\theta) \]
Thus, we can write:
\[ \cos(320^\circ) = \cos(360^\circ - 40^\circ) = \cos(40^\circ) \]

### Step 3: Use the Sine-Cosine Relationship
We also know the relationship between sine and cosine:
\[ \sin(\theta) = \cos(90^\circ - \theta) \]
For \( \theta = 40^\circ \):
\[ \sin(40^\circ) = \cos(90^\circ - 40^\circ) = \cos(50^\circ) \]
This means:
\[ \sin(50^\circ) = \cos(40^\circ) \]

### Conclusion
Thus, we can express \( \cos(320^\circ) \) in two ways:
1. \( \cos(320^\circ) = \cos(40^\circ) \)
2. \( \cos(320^\circ) = \sin(50^\circ) \)

### Final Answer
So, the expressions for \( \cos(320^\circ) \) as a function of angles between \( 0^\circ \) and \( 90^\circ \) are:
- \( \cos(40^\circ) \)
- \( \sin(50^\circ) \)